Finite Group Databasebeta

← #30599282

Subgroups — #30599282

Order 15616.

630 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461676C212yesmaximal
2#21460697C214yesmaximal, complemented
3#384×D61C211yesmaximal, characteristic
4C2×#14519844C2214yes—
5C2×#14519834—22no—
6#16840628—22no—
7C2×C4⋊C4×D61—22no—
8C2×C4⋊C4×D61C412yes—
9C2×C42×D61C2211yescharacteristic
10#16839632C411yescharacteristic
11#16839631—22no—
12#16839631C2212yes—
13C61×#384C411yescharacteristic
14C22×#92420—24no—
15#14519844—28no—
16#14519834—44no—
17C22×C4×D61—22no—
18C22×C4×D61C2×C411yescharacteristic
19C22×C4×D61D412yes—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61C2×C412yes—
22C2×#11758196—22no—
23C2×#11758196—24no—
24C4⋊C4×D61—44no—
25C4⋊C4×D61—44no—
26C4⋊C4×D61—44no—
27C2×C4×Dic61D412yes—
28C2×C4×Dic61C2311yescharacteristic
29C42×D61—24no—
30C2×C4⋊C4×C61—22no—
31C2×C4⋊C4×C61C2×C412yes—
32C2×C42×C61C2×C411yescharacteristic
33C23×D61C22⋊C411yescharacteristic
34C22×C4×C61—22no—
35C22×C4×C61C22⋊C412yes—
36C22×C4×C61C22×C411yescharacteristic
37C22×Dic61—22no—
38C22×Dic61C22⋊C411yescharacteristic
39C22×Dic61C2×D412yes—
40C2×C4×D61—22no—
41C2×C4×D61—22no—
42C2×C4×D61—22no—
43C2×C4×D61—24no—
44C2×C4×D61—24no—
45C2×C4×D61—44no—
46C2×C4×D61—48no—
47C2×C4×D61D814yes—
48C2×C4×D61SD1614yes—
49C2×#92420—44no—
50C2×#92420—44no—
51C2×#92420—44no—
52C4⋊C4×C61—42no—
53C4⋊C4×C61—44no—
54C42×C61—22no—
55C4⋊Dic61—44no—
56C4⋊Dic61—42no—
57#11758196—44no—
58#11758196—44no—
59#11758196—44no—
60C4×Dic61—24no—
61C4×Dic61#4114yes—
62C23×C61C2×C22⋊C411yescharacteristic
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—22no—
66C22×D61#10012yes—
67C22×D61#10214yes—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61—44no—
74C2×C4×C61#10214yes—
75C2×C4×C61#11712yes—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—42no—
79C2×Dic61—44no—
80C2×Dic61#10112yes—
81C2×Dic61#12314yes—
82C2×Dic61C2×D812yes—
83C2×Dic61C2×SD1612yes—
84C2×Dic61#13714yes—
85C4×D61—28no—
86C4×D61—28no—
87C4×D61—28no—
88C4×D61—88no—
89#92420—84no—
90#8723—611nomaximal, Sylow
91C22×C61#38111yescharacteristic
92C22×C61C2×#10011yescharacteristic
93C22×C61C2×#10111yescharacteristic
94C22×C61C2×#10212yes—
95C22×C61#41912yes—
96C2×D61—24no—
97C2×D61—22no—
98C2×D61—22no—
99C2×D61—24no—
100C2×D61#33114yes—
101C4×C61—22no—
102C4×C61—24no—
103C4×C61—82no—
104Dic61—22no—
105Dic61—82no—
106Dic61#48014yes—
107Dic61#48314yes—
108C2×#384—611no—
109#1797—612no—
110#1296—614no—
111C2×C61C2×#33111yescharacteristic
112C2×C61#154612yes—
113C2×C61#155811yescharacteristic
114C2×C61#182111yescharacteristic
115C2×C61#182312yes—
116D61—24no—
117C22×C4⋊C4—612no—
118C22×C4⋊C4—1222no—
119C22×C42—611no—
120C2×C4⋊C8—614no—
121C2×C22⋊C8—1222no—
122#384—612no—
123#384—611no—
124#384—1222no—
125#384#692311yescharacteristic
126#336—1222no—
127C61#872311yescharacteristic, complemented, Sylow
128C23×C4—612no—
129C23×C4—611no—
130C23×C4—1222no—
131C22×C8—1224no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—1222no—
135C2×C4⋊C4—1224no—
136C2×C4⋊C4—1222no—
137C2×C4⋊C4—2444no—
138C2×C4⋊C4—2444no—
139C2×C4⋊C4—2444no—
140C2×C4⋊C4C2×#692312yes—
141C2×C42—611no—
142C2×C42—612no—
143C2×C42—1224no—
144C2×C42C2×#692311yescharacteristic
145C4⋊C8—1228no—
146C22⋊C8—2444no—
147C24—611no—
148C22×C4—22no—
149C22×C4—612no—
150C22×C4—611no—
151C22×C4—614no—
152C22×C4—614no—
153C22×C4—1224no—
154C22×C4—1222no—
155C22×C4—1224no—
156C22×C4—1222no—
157C22×C4—1222no—
158C22×C4—1222no—
159C22×C4—2448no—
160C22×C4—2444no—
161C22×C4C22⋊#692312yes—
162C22×C4C22×#692311yescharacteristic
163C2×C8—2444no—
164C2×C8—2444no—
165C2×C8—2444no—
166C4⋊C4—42no—
167C4⋊C4—44no—
168C4⋊C4—2442no—
169C4⋊C4—2444no—
170C4⋊C4—2444no—
171C4⋊C4—2444no—
172C4⋊C4—2444no—
173C42—22no—
174C42—614no—
175C42—1224no—
176C23—612no—
177C23—614no—
178C23—1221no—
179C23—1221no—
180C23—1222no—
181C23C2×C22⋊#692311yescharacteristic
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—614no—
189C2×C4—612no—
190C2×C4—612no—
191C2×C4—614no—
192C2×C4—612no—
193C2×C4—1228no—
194C2×C4—1228no—
195C2×C4—1228no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—4888no—
199C2×C4—2442no—
200C2×C4—2444no—
201C2×C4#1451983914yes—
202C2×C4#1451985612yes—
203C8—4884no—
204C22—614no—
205C22—1224no—
206C22—1222no—
207C22—1222no—
208C22—1224no—
209C22#1684070511yescharacteristic
210C22D61⋊#10011yescharacteristic
211C22D61⋊#10111yescharacteristic
212C22C2×#1451983912yes—
213C22#1684075512yes—
214C4—22no—
215C4—24no—
216C4—82no—
217C4—614no—
218C4—614no—
219C4—1222no—
220C4—4882no—
221C2—1224no—
222C2D61⋊#33111yescharacteristic
223C2#2146132912yes—
224C2#2146135311yescharacteristic
225C2#2146171911yescharacteristic
226C2#2146172212yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#8723
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21460697C2semidirect
127. C61#8723semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214616762
#214606972
#384×D612
#872361